Line is defined by . Line is parallel to line m in the xy - plane and passes through the point (4, - 3). Which equation defines line p ?

The correct answer is:

Parallel lines are lines in a plane that are always the same distance apart. That means the points on both lines should be multiple of each other w.r.t. any one of the axes.
Moreover, if a line passes through a point, then putting in the coordinate value in the equation, would be satisfied.
Explanations:
Step 1 of 3:
Line m is defined by …(i)
Line p is parallel to line in the -plane and passes through the point .
Now, x = 4 in (i), we get
So, is a point situated on line m.
Step 2 of 3:
Since is a point situated on line , hence it must satisfy the equation.
Consider the equation given in option B,
Putting , we get
And that satisfies the equation for the point .
Step 3 of 3:
Observe that the coordinate for x-axis in case of both lines is same, viz. 4
But the coordinate for y-axis is different. For line m, it is -1 and for line p, it is -3.
That, in case, is a multiple of each other. Hence, it satisfies the condition for parallel lines, mentioned in the hint section.
Final Answer:
The equation defines line —